But I haven't paid too much attention to some mundane technical properties of the Bitcoin as a system to make payments. Well, the simplest shocking number I want you to pay attention to is that the average Bitcoin transaction costs you $10 in fees these days. It's virtually impossible to bring the fee beneath $5 – you may order cheaper transactions if you're willing to increase the confirmation waiting period by something in between hours and days. And it's a lot. It's a "wow", especially because the Bitcoin is often promoted as being a good method to make payments.

Among other things, the fact that the fee is some $10 implies that if your Bitcoin address has less than $10 on it, you can't get any money out of it at all! ;-) If you want to buy a $5 coffee with a Bitcoin, you will pay at least a tripled price due to the transaction fees. It's obviously not very practical.

But it's even more interesting to realize what it means for the idea that much of the mankind could use this particular Bitcoin to make payments in the future. Is it possible? The answer is a resounding No.

First, you should be reminded that the current number of Bitcoins is some 16.7 million. Some of them have been irreversibly lost, however. The total number approaches 21 million – the difference from 21 million shrinks exponentially (gets halved every 4 years). That's by the basic rules that Nakamoto randomly picked.

The derivative of the function above tells you that some 1,800 new Bitcoins are mined every day. The miners get some $13 million for that in new Bitcoins (yesterday, in 130 blocks per 24 hours, each of them rewarded by $100,000), assuming the current price around $7,100. Most of the miners are energy-efficient and they only pay 1/4 of their rewards for electricity – but they also had to buy the hardware which probably doesn't last forever and that's why the profitability is much less obvious than the "electricity as 1/4 of rewards" observation suggests. So some $3 million is paid for electricity every day – which means one billion dollars per year just for the electricity to mine the new Bitcoin.

Note that aside from the $3 million for miners' electricity, the miners get $10 million in new Bitcoins – to pay for other expenses (GPUs) and perhaps profit. Where does this wealth come from? Well, it's assumed that "wealth is created out of thin air" (the money comes from new real cash pumped into the Bitcoin bubble) despite the decreasing scarcity of the Bitcoins. But 1,800 new Bitcoins are 0.01% of the total number – which is some 3.65% per year. If the Bitcoins were stocks in a sensible stable company, the price of each stock should drop by those 3.65% a year. The annual changes of the Bitcoin price are higher by 2+ orders of magnitude so this 3.65% is unobservable in the chaos.

Every day, about 300,000 transactions occur (it was only 20% fewer a year ago, even though the Bitcoin price was 10 times lower). The average transaction fee is $10 as I mentioned so interestingly enough, the transactions cost some $3 million per day as well. If you transfer Bitcoins, you pay pretty much exactly for the electricity that has been wasted. $10 is really a lot of electricity, a modest apartment runs for a month and a house for a week. If you make a Bitcoin payment, you consume as much electricity as a modest apartment per month. Forget about savings on vacuum cleaners or TV etc. if you want to make some Bitcoin payment every month – the Bitcoin payment electricity wasting beats any electricity savings you can plausibly make. I've been sometimes running a Bitcoin mining software on my laptop for a month – I am extremely far from earning the money for one transaction fee so far. ;-)

So this is insane. Also, you may compare the wasted electricity by the Bitcoin mining in the world with millions of American households, with some less developed countries (Bitcoin devours more than Ecuador), with several big nuclear power plants etc. As the Financial Times wrote with some left-wing terminology, the environmental costs are not worth the candle. After I completed this blog post, I noticed that Nude Socialist wrote what a waste of resources a week ago, too. OK, everyone who is sane understands that lots of electricity is wasted for the Bitcoin and the wasting would get even worse if the Bitcoin were used by many more people. But let us look at the high transaction fees from another perspective.

Look at BitInfoCharts.com with lots of real-time data about the Bitcoin. You have hash rates, prices, rewards, difficulty, everything over there. You will also see that the average BTC transaction is worth $40,000 but the median one only $700 (the fee is over 1% for this median) – quite a difference between the average and the median. But let us look at the wealth distribution. How many addresses are there that are richer than X dollars? If X is something, then Y addresses:

$1: 14 million
$100: 4 million
$1,000: 2 million
$10,000: 0.5 million

You see a limited number of Bitcoin addresses. Note that only less than 10 million Bitcoin addresses have over $10 on them. The others have literally nothing because they can't even afford the fee for a single transaction. Because 10% fees are the maximum you could consider somewhat reasonable, you could say that only the Bitcoin addresses with at least $100 are remotely usable for payments, and there are just 4 million of them.

So the Bitcoin payment network may only be "at least somewhat reasonably" used by 4 million addresses. It's very likely that they're owned by a significantly smaller number of owners – because one owner typically has many Bitcoin addresses. I am no Bitcoin cultist but I have already had some Bitcoins on 4 addresses plus 4 addresses of other cryptocurrencies. ;-)

You may see that the number of people who can actually make any payments with the Bitcoin is at most comparable to one million. The number of addresses – including Tony's – that have over $10,000 on them is currently half a million. These people may trade with each other but by the basic design of the Bitcoin, they can't really extend the community of possible traders much because the fees are so high.

Could you increase the number of Bitcoin users who have some Bitcoins and can make reasonable payments to 100 million in coming years? The answer is negative once again. What would have to change to increase the number of people whose balance can "safely enough" beat the fees?

You could propose to keep the price comparable to the current price but reduce the fees. But that won't really happen. It's no coincidence that the fees are ultimately comparable to the electricity that is consumed. And the electricity that is consumed is some one quarter of the rewards given to the miners. They're linked to each other by the basic laws of economics. The miners pay something for the hardware i.e. GPUs, for the risk, and for electricity, and they still want to make some profit. This implies that the electricity is bound to cost some $3 million a day at current prices, or $1 billion per year, or 1% of the Bitcoin capitalization every year!

The system is simply designed in such a way that it naturally eats "its whole capitalization" in 100 years as of 2017. ;-) This wasteful number could improve and go to 200 years i.e. 0.5% a year in 4 years from now. But this number is extremely resilient. There are almost no parameters that could be adjusted and that could significantly change this conclusion.

Now, you could propose that things become better – easier to accommodate 100 million users – if the price of the Bitcoin goes up. But this hope can be easily seen to be flawed, too. Imagine that in 2018, the price of the Bitcoin goes to $100,000. Will this 14 times higher price make it easier to "pack" 100 million Bitcoin users into the capitalization? Once again, the answer is No. Why?

Because if the Bitcoin price quickly went up 14 times, so would the rewards for the miners expressed in U.S. dollars. Fees are some percentage of it that wouldn't deviate from the 1/4 as today much. So the total fees per day in U.S. dollars would go up 14 times, too. (Lots of new GPUs would probably be bought by the miners – the electricity consumption can't be too different from a multiple of the number of GPUs.) A question is what would happen with the number of transactions. If the number of transactions went up 14 times, you could keep the average fee at $10. If the number of transactions didn't increase, the average fee could be as much as $140 in a year.

As you could have noticed, the fees per transaction are so big basically because the fees expressed in BTC are completely fixed by the basic architecture of the Bitcoin payment system – and these big fees (billions of dollars per the year 2017) are divided among a relatively small number of transactions. The only thing that could make the fees "relatively" smaller – to allow more than "roughly one million" users – would be a vastly higher number of transactions. If the number of transactions were much higher, the difficulty of the mining tasks would decrease, and the blocks could contain a higher number of transactions. In effect, each transaction would be much cheaper.

Is it plausible that the fees will drop because the number of transactions will get much higher?

It seems extremely unlikely to me because the transaction fees are already high and they already discourage the Bitcoin users from making too many transactions. Again, note that some 8 million – about 1/2 – of the the Bitcoin addresses don't have enough money to pay for a single transaction, so they effectively have zero. An additional percentage only has a "somewhat more than the fee" and would waste most of the "money" for the fee. So you can't convince these "small money addresses" to make many more transactions than they're doing today – for most of them, one transaction is the last thing they can do.

On the other hand, the richer Bitcoin addresses, like Tony's, enjoy the concentration of the "money" and they don't want to fragment the capital too much because they realize that the transaction fees could become substantial, too. So don't expect any significant increase of the number of transactions that are already expensive. In other words, don't expect the transactions to get much cheaper!

So the whole Bitcoin "economy" is designed in such a way that the number of Bitcoins is limited and 1% of the capitalization is paid for fees. But that makes it very unattractive for the "small fish". So the celebrated "scarcity" directly implies that the Bitcoin network cannot have many more users than the current number. By the basic laws of mathematics – the answer is independent of virtually all the parameters that were unknown to Satoshi Nakamoto – it follows that in 2017, the number of users can't be too much higher.

What about the evolution of this conclusion with time? I mentioned that the difference between 21 million and the "current number of Bitcoins" gets halved every 4 years. So in 4 years from now, in late 2021, the miners will only get a smaller fraction of the Bitcoin capitalization (if any Bitcoin still exists) than now – they will mine 900 Bitcoins a day instead of today's 1,800. This could indeed change the mathematics, and effectively allow a higher number of "Bitcoin users who can afford the fee".

But even if you believe that all this "slowdown of the mining by 2021" to one-half of the current percentage allows you to reduce the fees, it's only by a factor of two. Instead of 4 million Bitcoin addresses that can reasonably afford the transaction fees, you could have 8 million Bitcoin addresses that can afford it in 2021. It's very clear that by 2021, you simply cannot make the Bitcoin a mainstream payment system in the U.S. or any major country. The mathematics directly prohibits it! You would need to wait to 2050-2100 or so for the numbers to allow the number of users who can afford the fees that is comparable to the U.S. or world population.

Again, there will only be less than 21 billion Bitcoins. The total fees are basically dictated by the pre-determined growth of the money supply, and they're 1% of the total capitalization of the Bitcoin going to miners annually. 0.25% of the capitalization goes to the electricity or equivalently fees. Because most of the transactions need the "small enough Bitcoin addresses", the fees are vastly higher percentages of the money on these addresses, and they're therefore discouraged from making many more transactions than today (it's literally impossible to afford more than 1 outgoing transaction for some 1/2 addresses today).

What would have to happen is for the rich Bitcoin users such as Tony to deliberately pay for lots of basically useless transactions. If they conspired to do it, they could drive the average transaction fee down, below the current $10. That would need quite some self-sacrifice from half a million of Tony-like holders who have more than $10,000 in Bitcoin. For this sacrifice by half a million Tonies to make an impact, they would have to increase the daily number of transactions (now 300,000) by another 500,000 or so. So Tony and everyone of his kind would have to make one transaction a day. At current fees, those would cost some $3,000 a year. Why would they be doing it?

So I think that pure mathematics and pure thought is enough to see that the Bitcoin simply cannot become a mainstream payment system for tens of millions of people in the next 5 years. The price is mostly dictated by some at most half a million of people – and this number won't grow too much, either – who hold a vast majority of the Bitcoin capitalization. Note that the statistics page contains another slicing of the wealth distribution. The top X addresses contain the Y percent of the Bitcoin capitalization:

10: 5%
100: 17%
1,000: 34%
10,000: 56%

It's really just 10,000 Bitcoin addresses that control a majority of the "Bitcoin wealth". The Bitcoin price growth has been governed by the increasing number of the "converted" people but one is gradually hitting a wall because too many small fish would own too little and the transaction fees would be too prohibitive for them.

So sometimes, approximately these days, the price growth starts to switch from the "dependence on the growing grass roots movement" to the "escalating fanaticism of the half a million users similar to Tony". For this reason, I think that even if the Bitcoin price kept on rising, the number of transactions would grow less quickly. The average transaction fee is proportional to the ratio of the Bitcoin capitalization and the number of transactions. So it's likely to grow above $10.

The relevant Bitcoin owners are some 0.5 or 1 million users – the number of humans behind them may be substantially smaller – who hold something that is claimed to be "the currency or payment system of the future" except that the transaction fees are $10 and they're basically guaranteed to grow if the Bitcoin price keeps on growing. As the average transaction fee becomes even (much) higher than $10 today, it's spectacularly clear that as time goes by, the Bitcoin becomes much less capable of becoming a mainstream payment system.

So why are these people fanatically hodling the virtual non-currency? Because they have become religious nut jobs who are ready to say an arbitrarily crazy thing (or insult) and sacrifice literally anything for their religion. The Bitcoin is unusable as a payment system, as a reliable storage of value. The fees are unacceptable today (even the 3-hour waiting for the confirmation is rather bad) and they would become even more unacceptable if the price continued to grow. That's why the rational limit of the capitalization – where it wasn't obvious that there's no way to turn the Bitcoin into a mainstream payment system – is already being hit, or has been hit. It has really been clear from the beginning but by now, everyone should be able to see what happens with the fees as the Bitcoin price goes up.

Of course, I can't predict the fanaticism of the folks like Tony. It may add another order of magnitude, indeed. But the claims that the Bitcoin is the "future of the money" may be almost rigorously proven – has been almost rigorously proven – to be ludicrous.

But if the likes of Tony have those $120 billion or so and they're fanatical, they can simply ignore the CME futures that will show the future BTC as worthless, and they may buy the real 16.7 million Bitcoins from everyone else at $7,000 or so. But once they do so, the number of transactions will plummet even relatively to today. The miners will still be getting huge rewards and with the tiny number of transactions, transaction fees may reach astronomical values. So Tony may own "many Bitcoins, perhaps 50" but it will be a "collectible" owned by 500,000 other fanatical "collectors" and to sell any fraction of the Bitcoins to another collector, you will have to pay a $1,000 fee. It doesn't look too attractive to me ;-) but of course some people may always behave in ways that others consider plain insane. In this scenario, it will be increasingly clear that a bunch of crazy "virtual collectors" is just paying some insane money to the miners who are immediately selling the newly mined Bitcoins to the collectors (with profit) because the miners actually aren't crazy. ;-)